Advances in Mathematical Physics

Volume 2015, Article ID 897120, 6 pages

http://dx.doi.org/10.1155/2015/897120

## Investigating the Nanoparticles Penetration Efficiency through Horizontal Tubes Using an Experimental Approach

College of Metrology and Measurement Engineering, China Jiliang University, Hangzhou, Zhejiang 310018, China

Received 6 October 2014; Revised 19 January 2015; Accepted 2 February 2015

Academic Editor: Alina Adriana Minea

Copyright © 2015 Zhaoqin Yin and Zhongping Dai. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

It is a complex transfer process of nanoparticles in a tube. In this paper, in order to quantify the penetration efficiency of nanoparticles in different flows condition through horizontal tubes, the experiments have been carried out with particles diameter between 6 nm and 560 nm in various lengths of sampling tube. The results were in good agreement with the theory of Gormley and Kennedy and the experiment results of Kumar et al. for particles size smaller than 100 nm. Particles penetration rate increases with increasing of the Schmidt number (Sc), and it decreases with increasing Reynolds and tube length. Particles deposition on the wall induces the changes of the mass and average diameter of particles continuously. Therefore, a nondimensional parameter (*ς*) defined dependency on Reynolds number and particle residence time in tube has been used to express total mass penetration efficiency and mean size growth rate through a straight tube.

#### 1. Introduction

Nanoparticles deposition inside tubes occurs in many important technological problems in biology, immunology, crystallization, and colloid and polymer science, such as enhanced heat transfer in heat exchangers [1], toxic particle transport in human lung contamination [2], pollutant particle emission from coal combustion in power plants, and the rail tube of a moving car [3]. For badly stable suspension of microsized particles, nanoparticles suspended inside a tube may coagulate or deposit on the wall due to various mechanisms that may act in combination with Brown motion and fluid turbulence [4]. The process of coagulation causes the particle clusters to grow up, and then the dynamic characteristics of large clusters are different from that of small clusters. There are five main mechanisms which may lead to particle losses on the surface of a tube, that is, gravitation, thermophoresis, electrostatics, inertial impaction, and diffusion [5]. The diffusion, inertial impaction, and turbulence are most important for deposition process. When nanoparticles deposit on the tube wall, the characteristics of the delivery particles such as number and mass concentration, average diameter, and size distribution will be changed. However, the mechanism of deposition and evolution of the nanoparticles still remains to be clarified.

In recent years the transport and deposition processes of nanoparticles in tube are of increasing concern since nanoparticles are more toxic and diffusible than larger particles. The analyses of the forces acting on nanoparticle in flow and its deposition processes have been made by many researchers [6–8]. The research of particle deposition has been studied, such as in bends [6] and a rotating curved tube [9], respectively. Numerous authors have developed theoretical expression for aerosol penetration fraction through a smooth or rough tube in laminar flow [10]. Several experimental validations of these theories have been carried out for aerosols particles with diameters smaller than 100 nm [11]. For turbulent tube flow, the deposition onto tube surfaces is more complicated and equations describing it cannot be solved explicitly, and these studies give very different results [8, 12].

The number penetration efficiency through a tube is defined as the ratio of outlet number concentration to inlet concentration, which is where is the number concentration per cubic meter.

Gormley and Kennedy [10] firstly developed laminar flow through a straight cylindrical tube as a function of a dimensionless deposition coefficient of particle sizes ranging from 3 to 50 nm. The well-known equation iswhere , is the tube inner diameter, and is the flow residence time in the tube. is the diffusion coefficient, given by Stokes-Einstein equation:
where (= 1.38 × 10^{−23} J K^{−1}) is Boltzmann’s constant, is the absolute temperature, is the viscosity of air, is the slip correction factor, and is the aerodynamic diameter of particles. Allen and Raabe [13] developed the slip correction factor for solid particles for all size ranges, which is
where is the particle mean free path.

Hinds [14] simplified the equation, and Ramamurthi et al. [15] and Alonso et al. [16] confirmed the accuracy of the above equation. Noble et al. [17] measured particles in a continuous field measurement for laminar flow using scanning mobility particle sizers (SMPS) (TSI Inc.) and aerodynamic particle sizer (APS) (TSI Inc.) through a 3 m long aluminium tube with slight bends for connections to the sampling instruments. Their results show that the penetration efficiency was substantially smaller than the theoretical penetration efficiency.

When Reynolds number is larger than 2300, the flow is in the turbulent tube flow condition. The deposition on tube surface is more complicated than a laminar flow. Lee and Gieseke [12] presented a penetration empirical equation of particles through a tube considering diffusion, inertial impaction, and turbulence, which is where is diffusive deposition velocity through the laminar sublayer for turbulent flow in a tube, , is the tube length, and is the density of the particle. is the flow Reynolds number based on the pipe diameter and average flow velocity and is the fluid volumetric flow rate in tube.

Equation (8) is only significant for particles larger than 100 nm. Kumar et al. [11] studied particles losses in sampling tube of various lengths on typical diesel car exhaust emissions and compared penetration efficiencies with particle loss models of laminar and turbulent flows. Their results show that when the flow is laminar, the turbulent penetration model of Lee and Gieseke [12] is better than the laminar model of Hinds [14].

Since the results of the previous studies are incompatible and insufficient, the mechanisms of the nanoparticle deposition in tube should be clarified more deeply for its important application. Therefore, the aim of this study is to investigate the nanoparticles mass and number concentration penetration efficiency through different flow conditions tubes using an experimental approach.

#### 2. Experimental Techniques

Ignore thermophoresis and electrostatics effect on nanoparticles and coagulation process. Assume that only diffusion, inertial impaction, and turbulence have the impact on deposition process. Experiments were made under different flow conditions. A sketch of the experimental setup is shown in Figure 1. The nanoparticles are generated by aerosol generator. The compressed air has been cleaned by a filter. Particles and compressed air have been mixed in a pressure chamber and placed twenty-four hours for mixture uniform in the vessel. The flow required for the tube is regulated using a valve downstream of the mixing chamber. In order to obtain a fully developed flow profile, there is a sufficient length between valve A and valve B. Between valve B and valve C and valves B, C, and D there are three-way valves used to regulate the fluid flow rate and direction. When the fluid passes through valves A, B, and D and a fast mobility particle sizer (FMPS3091, TSI Inc.), the entrance parameters are measured. When the aerosol passes through valves A and B, the sampling tube, valve C, valve D, and FMPS3091, the exit parameters are measured. The sampling tube is made of plexiglass and measurements are carried out in the laboratory with temperature of 20°C.